The invention relates to an iterative method for in each one of a sequence of iterating cycles, firstly short-time-Fourier-transforming a speech signal, and secondly resynthesizing the speech signal from a modulus (expression 2) derived from its short-time Fourier transform, and in an initial cycle additionally from an initial phase, until the sequence produces convergence. A successful iteration sequence produces a time-varying or constant signal that has a transform or spectrogram which is quadratically close to the specified spectrogram. The spectrogram itself is a good vehicle for speech processing operations. Such a method has been disclosed in D. W. Griffin and J. S. Lim, `Signal Estimation from Modified short-time Fourier Transform`, IEEE Transactions on ASSP, 32, No.2 (1984), 236-243. The known method uses a random phase for the resynthesizing; it has been found that the cost function generated in this manner may have many local minima. It is thus impossible to guarantee convergence to the global optimum, and the final result depends heavily on the initial phase actually used.